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Age-dependent intra-specific competition in pre-adult life stages and its effects on adult population dynamics

Published online by Cambridge University Press:  12 August 2015

RONGSONG LIU ,
GERGELY RÖST  and
STEPHEN A. GOURLEY
RONGSONG LIU
Affiliation:
Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, 82071, WY, USA email: Rongsong.Liu@uwyo.edu
GERGELY RÖST
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary email: rost@math.u-szeged.hu
STEPHEN A. GOURLEY
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK email: s.gourley@surrey.ac.uk
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Abstract

Intra-specific competition in insect and amphibian species is often experienced in completely different ways in their distinct life stages. Competition among larvae is important because it can impact on adult traits that affect disease transmission, yet mathematical models often ignore larval competition. We present two models of larval competition in the form of delay differential equations for the adult population derived from age-structured models that include larval competition. We present a simple prototype equation that models larval competition in a simplistic way. Recognising that individual larvae experience competition from other larvae at various stages of development, we then derive a more complex equation containing an integral with a kernel that quantifies the competitive effect of larvae of age ā on larvae of age a. In some parameter regimes, this model and the famous spruce budworm model have similar dynamics, with the possibility of multiple co-existing equilibria. Results on boundedness and persistence are also proved.

Keywords

Competitionlarvajuvenilestage-structuredelaystability
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 1 , February 2016 , pp. 131 - 156
Copyright
Copyright © Cambridge University Press 2015 

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